To see why [1]} is a special case of our framework, note that the total variation distance between two random variables is at most the probability of disagreement under any coupling. [1]} uses the same quantization randomness (used for training) for verifying after the edit request - this corresponds to a trivial coupling between the quantization randomness, hence the total variation distance between the outputs is bounded by the upper bound on the probability that the quantized points change (see claim:quantize). This establishes that it is a TV stable method. Finally, as said before, using the same quantization randomness corresponds to a trivial coupling, but can be shown to be maximal since the probability distribution is uniform around the to-be-quantized point. Therefore, we have that [1]} uses a maximal coupling based unlearning method.
